Table 3. Simulation results for LRTS under alternative distributions.

MOI	Method to calculate power	Simulation Power *			KS-Test P-value
		10−3 Level	10−4 Level	10−5 Level
Dosage	Simulation	0.958 (0.946, 0.970)	0.866 (0.845, 0887)	0.735 (0.708, 0.762)	0.01
	Asymptotic	0.949	0.856	0.712
Extremes	Simulation	0.950 (0.936, 0.964)	0.857 (0.835, 0.879)	0.738 (0.711, 0.765)	0.07
	Asymptotic	0.946	0.848	0.700

Legend for Table 2. Based on 1000 replications and 200 sample size per case/control group.

^*95% approximate confidence intervals for simulated power are given in parentheses.

Here, we present simulated and asymptotic power for the LRTS when the alternative hypothesis that mixing proportions are different in each of two groups is true. The mixing proportions are computed using equations (4) for the Dosage and Extremes models, where CNP population frequencies are as specified above (Methods - Genetic model parameters for efficiency analysis). For the Dosage model, the relative risks are: R ₂ = 1.8, R ₃ = 1.8² = 3.64, R ₄ = 1.8³ = 5.83. For the Extremes model, the relative risks are: R ₁ = 1, R ₂ = 0.3, R ₃ = 0.3, R ₄ = 1. Asymptotic power is computed using the non-centrality parameter documented in equation (A1). The column “KS-Test P-value” refers to the p-value computed using the Kolmogoroff-Smirnoff goodness of fit test, as implemented in R programming environment.